Impulsive Control Design Of Stochastic Multi-valued Logical Networks

Stochastic systems are of great importance in modern control theory.As a special kind of stochastic systems,stochastic multi-valued logical networks(SMVLNs)have been widely applied in the field of biology,medical science and so on.Considering the impact of impulsive phenomenon in practical systems,impulsive SMVLNs have important research value.This paper studies the impulsive control design of SMVLNs.Firstly,using the algebraic state space representation(ASSR)method,the transition probability matrix of impulsive SMVLNs is established.A kind of finite step reachability matrix with probability one is constructed,based on which,several effective criteria are proposed for the finite-time controllability with probability one of impulsive SMVLNs.A necessary and su cient condition is presented for the finite-time set controllability with probability one of impulsive SMVLNs by constructing the set controllability probability distribution vector,and the obtained results are extended to the switching topology case.Secondly,a novel system with augmented control is established by regarding the impulsive time as a special kind of control,which is equivalent to the considered impulsive SMVLNs.A necessary and su cient condition is proposed to design impulsive control for the output tracking problem of impulsive SMVLNs.Moreover,a constructive method is put forward to design the state feedback controller and state-dependent impulsive time sequence.Thirdly,a constructive method is proposed to design time-variant state feedback controller for the set stabilization of impulsive SMVLNs.Furthermore,the obtained results are applied to both state synchronization and output synchronization of master-slave impulsive SMVLNs.Finally,the obtained results are applied to the impulsive SMVLNs modeled by real biological networks,such as lactose operon,to verify the effectiveness.